Q. Consider the line integral
∫(𝑥𝑑𝑦 − 𝑦𝑑𝑥)
𝐶
the integral being taken in a counterclockwise direction over the closed curve 𝐶 that forms the boundary of the region 𝑅 shown in the figure below. The region 𝑅 is the area enclosed by the union of a 2 × 3 rectangle and a semi-circle of radius 1. The line integral evaluates to
(A) 6 + 𝜋/2
(B) 8 + 𝜋
(C) 12 + 𝜋
(D) 16 + 2𝜋
Ans: 12 + π
Solution:
